Anal. Chem. 2007, 79, 1237-1242
pH-Independent Fluorescent Chemosensor for Highly Selective Lithium Ion Sensing Daniel Citterio,*,† Junichiro Takeda,† Masaki Kosugi,† Hideaki Hisamoto,†,‡ Shin-ichi Sasaki,†,§ Hirokazu Komatsu,† and Koji Suzuki†,|,⊥
Department of Applied Chemistry, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan, Kanagawa Academy of Science and Technology (KAST), KSP West, 3-2-1 Sakado, Takatsu-ku, Kawasaki 213-0012, Japan, and Core Research for Evolutional Science and Technology (CREST), JST Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
Since lithium salts are used as pharmaceutically active compounds against manic-depressive psychosis, there is a demand to monitor the lithium concentration in blood in the narrow range of 0.6-1.2 mM effectively and safely. Here we report on an optical sensor approach for the determination of Li+, based on the design and synthesis of a novel lithium fluoroionophore KLI-1 and its polymer immobilizable derivative KLI-2, and the application to an optode. The novel lithium fluoroionophores rely on a tetramethyl “blocking subunit” bearing 14-crown-4 as a Li+-selective binding site and 4-methylcoumarin as a fluorophore, intramolecularly connected to show ICT-type wavelength shift for ratiometric fluorescence measurements. The fluoroionophores showed high selectivity for Li+ with binding-induced blue shift in the fluorescence spectra, no response to major biological interfering cations (K+, Ca2+, Mg2+), a selectivity of log kLi+,Na+ ) -2.4 over Na+ in solution, and no response to pH in the range of pH 3-10. A hydrophilic optode membrane with KLI-2 immobilized also showed good selectivity for Li+, pH independence in the physiological range (pH 6-8), and fully reversible signal changes. KLI-1 and KLI-2 are excellent Li+ fluorescent chemosensors that can be applied to quantitative measurements of lithium in clinical samples, although possible interference from Na+ has to be considered at the lower therapeutic level of Li+. Lithium ions belong to the group of the five biologically most important alkali and alkaline earth metal cations. Lithium-containing drug preparations are routinely used in medical and clinical applications for the treatment of manic-depressive psychosis. In many cases, patients are required to take the drug over periods of several months or even years. The concentration of lithium ions in blood serum after drug intake varies strongly from person to * Corresponding author: (e-mail)
[email protected]; (phone) +8145-566-1566; (fax) +81-45-566-1566. † Keio University. ‡ Present address: Graduate School of Material Science, University of Hyogo, 3-2-1 Kouto, Kamigori, Hyogo 678-1297, Japan. § Present address: Department of Bioscience and Biotechnology, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan. | Kanagawa Academy of Science and Technology. ⊥ Core Research for Evolutional Science and Technology. 10.1021/ac061674g CCC: $37.00 Published on Web 11/30/2006
© 2007 American Chemical Society
person and has to be monitored in the individual patient regularly. In this context, the reliable determination of the lithium ion concentration levels in blood samples is important for successful and safe therapeutic applications, since too low levels show no effect at all and an overdose of lithium can lead to life-threatening toxic effects. Lithium ion concentrations in serum during the treatment should be within the narrow range of 0.6 and 1.2 mM.1,2 At present, the most widely used instruments for clinical lithium determinations are based on ion-selective electrodes (ISEs) applied to a serum sample directly or after dilution with a buffer solution.3-5 Optical instruments offer some advantages compared to their electrochemical counterparts. They are not sensitive to electromagnetic interference, are easier in maintenance due to the lack of a reference electrode, and have a great potential for miniaturization as well as low-cost mass production.6,7 Simple portable instruments are useful for point-of-care testing or even home use since they allow independent use from a clinical laboratory by personnel minimally trained. Many optical ion sensing schemes of high selectivity are based on ion-exchange or ion-coextraction systems, where protons are involved in addition to the target analyte ion.8-10 Such systems rely on the active mass transport of the target ion from the aqueous sample phase into a lipohilic organic polymer membrane phase. In these so-called bulk optodes, a thermodynamic equilibrium between the sample phase and the entire membrane phase is established. The degree of mass transport is determined by the ion recognition compounds and additives incorporated into the membrane phase. The ion extraction into the organic phase occurs due to complex formation with an ionophore incorporated into the bulk membrane. The advantage of these systems is the fact that the same ionophores known for ISEs can be applied.4 A lipophilic pH indicator added to the membrane phase acts as an (1) Jope, R. S. Mol. Psychiatry 1999, 4, 117-128. (2) Manji, H. K.; Potter, W. Z.; Lenox, R. H. Arch. Gen. Psychiatry 1995, 52, 531-543. (3) Bakker, E.; Bu ¨ hlmann, P.; Pretsch, E. Chem. Rev. 1997, 97, 3083-3132. (4) Bu ¨ hlmann, P.; Pretsch, E.; Bakker, E. Chem. Rev. 1998, 98, 1593-1687. (5) Gadzekpo, V. P. Y.; Moody, G. J.; Thomas, J. D. R.; Christian, G. D. Ion Sel. Electrode Rev. 1986, 8, 173-207. (6) Hisamoto, H.; Suzuki, K. Trends Anal. Chem. 1999, 18, 513-524. (7) Spichiger-Keller, U. E. Chemical Sensors and Biosensors for Medical and Biological Applications; Wiley-VCH: Weinheim, 1998. (8) Suzuki, K.; Tohda, K.; Tanda, Y.; Ohzora, H.; Nishihama, S.; Inoue, H.; Shirai, T. Anal. Chem. 1989, 61, 382-384.
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optical transducer.11-13 The changes of optical properties of the bulk ion-exchange optode are induced by an exchange of protons against sample cations and the concurrent protonation or deprotonation of the pH indicator in the optode membrane. In order to maintain the electroneutrality, the addition of lipophilic ionic additives is required in some cases. The measured optical signal does not reflect the target ion activity alone, but rather the ratio of the ion activity and the proton activity. For this purpose, the pH of the sample has to be measured simultaneously or it has to be kept constant by the means of buffer solutions. In order to facilitate the measurement and to increase the accuracy, pHindependent optical sensors are of high interest.3,4,14 The molecular design of ionophores for selective complexation of Li+ was thoroughly investigated in our laboratory and by others.3,4,15,16 It was found that the tetramethyl-14-crown-4 (TM14C4) skeleton bearing sterically blocking subunits showed excellent selectivity for Li+ over Na+ (log kp°tLi+,Na+ ) -2.6). In addition, several chromoionophores and fluoroionophores for Li+ have been reported;17-20, however, they show limited selectivities17,18 or pH sensitivity19 or they are only applicable in organic solvents.18,20,21 In this paper, we present the development and the application of a highly selective lithium fluoroionophore having a tetramethylsubstituted 14-crown-4 ether (TM14C4) as the selective binding site that shows pH independent optical properties. A polymer film with immobilized Li-fluoroionophore was developed for sensing applications in aqueous environment as an optode with high potential for practical applications. Other optical lithium sensing schemes have been described by our group earlier.22-25 However, all of these rely on a two-phase, ion-exchange system as described above and, as a consequence, are dependent on sample pH values. Therefore, in order to make full use of the pH independence of our newly developed fluoroionophore, in the optical sensor described in this report, both binding and fluorescence signal transduction take place in a hydrophilic environment with no need for ion exchange. (9) Seiler, K.; Simon, W. Anal. Chim. Acta 1992, 266, 73-87. (10) Bakker, E.; Simon, W. Anal. Chem. 1992, 64, 1805-1812. (11) Bakker, E.; Lerchi, M.; Rosatzin, T.; Rusterholz, B.; Simon, W. Anal. Chim. Acta 1993, 278, 211-225. (12) Citterio, D.; Jenny, L.; Spichiger, U. E. Anal. Chem. 1998, 70, 3452-3457. (13) Hisamoto, H.; Tani, M.; Mori, S.; Yamada, T.; Ishigaki, T.; Tohma, H.; Suzuki, K. Anal. Chem. 1999, 71, 259-264. (14) Krause, C.; Werner, T.; Huber, C.; Wolfbels, O. S.; Leiner, M. J. P. Anal. Chem. 1999, 71, 1544-1548. (15) Suzuki, K.; Yamada, H.; Sato, K.; Watanabe, K.; Hisamoto, H.; Tobe, Y.; Kobiro, K. Anal. Chem. 1993, 65, 3404-3410. (16) Kobiro, K.; Hiro, T.; Matsuoka, T.; Kakiuchi, K.; Tobe, Y.; Odaira, Y. Bull. Chem. Soc. Jpn. 1988, 61, 4164-4166. (17) Chenthamarakshan, C. R.; Ajayaghosh, A. Tetrahedron Lett. 1998, 39, 17951798. (18) Erk, C¸ .; Go ¨c¸ men, A.; Bulut, M. Supramol. Chem. 1999, 11, 49-56. (19) Shibutani, Y.; Sakamoto, H.; Hayano, K.; Shono, T. Anal. Chim. Acta 1998, 375, 81-88. (20) Thompson, J. C. Clin. Chim. Acta 2003, 327, 149-156. (21) Qin, W.; Obare, S. O.; Murphy, C. J.; Angel, S. M. Anal. Chem. 2002, 74, 4757-4762. (22) Watanabe, K.; Nakagawa, E.; Yamada, H.; Hisamoto, H.; Suzuki, K. Anal. Chem. 1993, 65, 2704-2710. (23) Hirayama, E.; Sugiyama, T.; Hisamoto, H.; Suzuki, K. Anal. Chem. 2000, 72, 465-474. (24) Suzuki, K.; Hirayama, E.; Sugiyama, T.; Yasuda, K.; Okabe, H.; Citterio, D. Anal. Chem. 2002, 74, 5766-5773. (25) Kurihara, K.; Ohtsu, M.; Yoshida, T.; Abe, T.; Hisamoto, H.; Suzuki, K. Anal. Chim. Acta 2001, 426, 11-18.
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Figure 1. Chemical structures of the Li+-selective fluoroionophores KLI-1 (R ) CH3) and KLI-2 (R ) (CH2)4sCHdCH2).
EXPERIMENTAL SECTION Synthesis. The synthesis of the lithium fluoroionophores KLI-1 and KLI-2 is described in the Supporting Information. Reagents. The highest grade commercially available reagents were used for the preparation of aqueous test electrolytes (chloride salts) and pH buffer solutions. The deionized water used had a resistivity of greater than 1.5 × 107 Ω cm at 25 °C. The monomers, initiator, and cross-linker used for the preparation of the sensing membranes were all obtained from commercial sources and used as received. Instruments. The absorbance spectra of dissolved dye solutions were recorded on a Hitachi U-2001 double-beam spectrophotometer (Hitachi Co., Ltd., Tokyo, Japan). Fluorescence emission spectra were measured at 25 ( 1 °C on a Hitachi F-4500 spectrophotometer using either a standard fluorescence quartz cell (d ) 1 cm) in a temperature-controlled cell holder (dissolved dye solutions) or a temperature-controlled loop injector (8 mL) autosampling system and a small-volume flow cell (Figure S-1, Supporting Information) constructed in our laboratory (sensing membranes). Samples were delivered to the flow cell in a constant flow of 1 mL/min using an HPLC pump system and deionized water. Preparation of Dissolved Dye Sample Solutions. Due to the limited solubility of the fluoroionophore KLI-1 in water, samples were prepared by first dissolving the dye in methanol and then diluting with water to obtain samples with a final concentration of 5.0 × 10-6 M KLI-1 in water/methanol 99:1. Preparation of Sensing Membranes. Hydrophilic polymeric sensing membranes containing the Li+-fluoroionophore KLI-2 were prepared from a membrane cocktail consisting of 6.7 parts (all parts by weight) of poly(ethylene glycol) dimethacrylate (PEGDMA) (n ) 16), 6.7 parts of 2-hydroxyethyl methacrylate (HEMA), 20.0 parts of N-vinyl-2-pyrrolidone (N-VP), 6.7 parts of dimethylacrylamide (DMAA), and 0.25 parts of KLI-2 dissolved in 40.0 parts of DMSO and 20.0 parts of H2O, while adding 0.2 parts of azobisisobutytonitrile as polymerization initiator. Several drops of this membrane cocktail were transferred to a glass support and covered with a quartz plate, using a microscope cover glass (thickness 1 mm) on each side to keep the distance between the cover and the base support. Subsequent thermal copolymerization was performed by placing the glass support into an oven while heating at 60 °C for 45 min. Finally, the resulting membranes were removed from the glass support by soaking in methanol. They were washed thoroughly with water and methanol. RESULTS AND DISCUSSION Design Principle for the Li+-Selective Fluoroionophores. The chemical structures of the novel fluoroionophores KLI-1 and KLI-2 presented in this study are shown in Figure 1. The design of the ion binding crown ether unit is based on the introduction
Figure 2. Changes in the fluorescence emission spectra of KLI-1 upon the addition of LiCl in H2O/methanol 99:1; [KLI-1] ) 5.0 × 10-6 M; excited at 340 nm.
of bulky substituents acting as blocking walls in order to prevent the formation of sandwich-type complexes with larger cations not fitting into the crown cavity. At the same time, these blocking units increase the rigidity of the crown ether ring and reduce the possibility of the formation of wrapping-type complexes with smaller cations. This principle has been described by our group before and was successfully applied to the development of highly selective ionophores for use in ISEs for Li+,15, 16 Na+,26 and NH4+.27 The selected crown ether contains no proton ionizable groups in order to guarantee a pH-independent ion binding. For the fluorophore moiety, a coumarin structure was chosen due to the pH independence over a wide pH range and the bright fluorescence. Several coumarin-bearing crown ethers without further selectivity enhancing substituents have been previously prepared by Erk and co-workers.18,28-30 For some compounds, iondependent fluorescence emission spectra in acetonitrile solution have been demonstrated. The 6,7-substituted macrocyclic coumarin derivatives show spectral changes according to the principle of photoinduced intramolecular charge transfer (ICT), where the crown ether oxygen heteroatoms are assumed to act as electrondonating sites and the keto group of the coumarin moiety as electron-accepting site. Therefore, the binding of a positively charged cation in the crown ether ring is expected to result in a spectral blue shift due to the destabilizing interaction between the positive charge of the guest cation and the partially positive charged oxygen centers of the guest. Spectral Properties of KLI-1. The fluorescence emission intensities of KLI-1 are strongly dependent on the solvent polarity. A strong increase in the intensity is observed with increase in the polarity of the solvent from acetone to methanol, accompanied by a small red shift of 7 nm of the emission band (Figure S-2, Supporting Information). The result makes this type of fluoroionophore useful for applications in polar media such as aqueous solutions. (26) Suzuki, K.; Sato, K.; Hisamoto, H.; Siswanta, D.; Hayashi, K.; Kasahara, N.; Watanabe, K.; Yamamoto, N.; Sasakura, H. Anal. Chem. 1996, 68, 208215. (27) Suzuki, K.; Siswanta, D.; Otsuka, T.; Amano, T.; Ikeda, T.; Hisamoto, H.; Yoshihara, R.; Ohba, S. Anal. Chem. 2000, 72, 2200-2205. (28) Bulut, M.; Erk, C¸ . Synth. Commun. 1992, 22, 1259-1263. (29) Go ¨c¸ men, A.; Bulut, M.; Erk, C¸ . Pure Appl. Chem. 1993, 65, 447-450. (30) Erk, C¸ .; Go¨c¸ men, A.; Bulut, M. J. Inclusion Phenom. Mol. Recognit. Chem. 1998, 31, 319-331.
Figure 3. Ratiometric fluorescence emission signal (I426 nm/I380 nm) obtained with KLI-1 in water/methanol 99:1 (a) in the presence of Li+(b), Na+(3), K+(4), Mg2+(+), and Ca2+(O) as Cl- salts and (b) for various pH values; [KLI-1] ) 5.0 × 10-6 M; excitation at 340 nm.
Sensing Properties of KLI-1 in Aqueous Solution. Figure 2 shows the Li+-concentration-dependent fluorescence emission spectra of KLI-1 in water/methanol 99:1. The absorption spectra are indifferent to changes in the lithium content (Figure S-3, Supporting Information). The fluorescence emission spectra show a small blue shift with an isoemissive point at 401 nm as expected based on the ICT theory for fluoroionophores. A Li+-concentrationdependent quenching of the main emission band at 426 nm is observed accompanied by an increasing intensity of the shoulder at 380 nm. Although this is only a minor shoulder, its appearance allows the ratiometric processing of the intensity data at two different wavelengths, which is a significant advantage over systems relying on the emission intensity of a single peak alone. The influence of possible interfering ions such as sodium, potassium, magnesium, and calcium present in clinical samples was investigated. From the data shown in Figure 3a, a selectivity coefficient log kLi+,Na+ of -2.4 was estimated. This figure is reasonably close to the value observed for an ion-selective electrode based on a tetramethyl-14-crown-4 derivative (log kp°tLi+,Na+ ) -2.6).15 When comparing the two values, it has to be noted that the selectivity coefficient determined for KLI-1 in solution purely reflects the differences in the complex formation constants between the fluoroionophore and the lithium and sodium ion, respectively. The potentiometric selectivity coefficient, however, additionally reflects the ion-exchange constant for the distribution of the lithium and the sodium ion between the Analytical Chemistry, Vol. 79, No. 3, February 1, 2007
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Figure 4. Li+-concentration-dependent response curves: (b) KLI-1 (normalized emission ratio; data extracted from Figure 3); (9) KLI-2 (normalized emission intensity; data extracted from Figure 5). The solid lines are based on a curve fitting with theoretically calculated equilibrium constants assuming a 1:1 complex formation (log K (KLI1) ) 2.80; log K (KLI-2) ) 1.95).
aqueous sample phase and the organic membrane phase, where the ion binding occurs.31 Due to the higher hydrophilicity of the lithium ion, its phase transfer into the organic membrane phase is disadvantaged compared to the sodium ion. Accordingly, the binding selectivity of the receptor itself appears to be slightly better for the ISE membrane, compared to the fluoroionophore in aqueous solution. The divalent cations Ca2+ and Mg2+ did not induce any response of the sensor within the investigated concentration range. Reasonably assuming a 1:1 complex formation between the ion binding crown ether moiety and the Li+ ion, a binding constant of log K ) 2.80 (Figure 4) was estimated for KLI-1 in water/methanol 99:1 based on a curve-fitting procedure applied to the experimental data presented in Figure 3a. The fluoroionophore responded to Li+ ions in concentrations from below 0.1 to above 10 mM. The influence of changing pH values on the response of KLI-1 was investigated. Due to the absence of a proton ionizable group in the fluoroionophore structure, no response to pH was observed over a wide pH range from 3 to 10. The data for the physiologically important pH range between 6 and 8 are shown in Figure 3b. Thus KLI-1 can be stated to have high Li+ selectivity in an aqueous environment compared to interfering ions encountered in clinical use and is not influenced by changes in pH value. Optode Membrane for Continuous Measurements of Li+ in 100% Water. KLI-1 showed excellent selectivity for Li+ as mentioned above; however, its low solubility in a 100% aqueous environment considerably limits its analytical applicability. For this reason, a modified derivative KLI-2 was synthesized having an unsaturated alkyl chain as immobilizing site to a polymer membrane, rendering the compound useful for application in an optode-type sensor. Hydrophilic polymer optode membranes that do not rely on an ion-exchange mechanism are preferable for small hydrophilic ions such as Li+ and in particular for obtaining pH independence. Various copolymer compositions were evaluated, and the membrane based on a matrix of three monomers (N-VP, HEMA, DMAA) and a cross-linker PEGDMA (n ) 16) was found (31) Bakker, E.; Meruva, R. K.; Pretsch, E.; Meyerhoff, M. E. Anal. Chem. 1994, 66, 3021-3030.
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Figure 5. Continuous changes in fluorescence emission intensity of KLI-2 covalently immobilized to an optode membrane monitored at 425 nm (excitation at 342 nm) upon subsequent exposure to deionized water and not pH-buffered aqueous Li+ solutions of various concentrations (0.16 , 0.1, 0.08, 0.06, 0.04, and 0.02 M, and 16, 10, 8, 6, 4, 2, and 1 mM; continuous sample flow of 1 mL/min).
to be most suitable. In the search for the most suitable composition, materials used for the production of soft contact lenses were preferably investigated, since they are known for their hydrophilicity, optical transparency, and mechanical stability. The finally obtained membrane was optically transparent at wavelengths above 330 nm and showed sufficient mechanical stability for sensing purposes, allowing the membrane to be set in a flow cell. The membrane-immobilized fluoroionophore showed a fluorescence excitation maximum at 342 nm and a fluorescence emission maximum at 425 nm. Those wavelengths are almost identical to the spectral data obtained with KLI-1 in water/methanol 99:1 solution and indicate that the immobilized fluoroionophore is located in a highly polar environment. Furthermore, the identical shape of the emission bands of KLI-1 in water/methanol 99:1 solution (5.0 × 10-6 M; Figure 2) and KLI-2 immobilized to the polymer membrane (spectra not shown) allows the conclusion that the covalent attachment of KLI-2 does not alter its spectral properties and does not result in an aggregation of dye molecules in the polymer. Figure 5 shows the response of the optode membrane upon exposure to deionized water and not pH-buffered aqueous Li+ solutions of various concentrations in a continuous flow system. The sensor responded to Li+ ions in concentrations from below 1 mM to above 160 mM. From the data in Figure 5, a detection limit of 0.6 mM Li+ was estimated based on the threefold noise level recorded for the baseline signal. The measurement in descending concentration order with intermediate water flushing demonstrates the full recovery of the emission signal up to the baseline, without any influence remaining from the previous sample. From the direct comparison of the response curves plotted in Figure 4, it can be seen that the response range of the membrane-bound fluoroionophore KLI-2 is shifted to higher concentrations compared to KLI-1 in solution. In the case of KLI2, a binding constant of log K ) 1.95 was estimated, again assuming a 1:1 complex formation with the Li+ ion. This 7-fold decrease in the binding strength for the membrane-immobilized fluoroinophore is assumed to be influenced by the reduced degree of freedom of the binding site in the more rigid membrane
Figure 6. Continuous changes in fluorescence emission intensity of KLI-2 covalently immobilized to an optode membrane upon repeated injections of aqueous 0.1 M Li+ solutions (not pH buffered) in the presence of various concentrations of possibly interfering cations (emission monitored at 425 nm; excitation at 342 nm).
environment compared to the solution. Furthermore, although a hydrophilic membrane material is used, the microenvironment in the polymer network is still less hydrophilic than in water/ methanol 99:1 solution, influencing the transition of the strongly hydrated Li+ ion from the aqueous sample solution into the polymer. The selectivity of the membrane sensor over possible interfering ions was evaluated by exposing the optode to mixed solutions of 1 mM, 10 mM, and 0.1 M Li+ in the presence of sodium, potassium, magnesium, or calcium ions at 0.01 or 0.1 M concentrations with intermediate rinsing with deionized water, while being continuously excited at 425 nm. The corresponding emission signal for 0.1 M Li+ solutions is shown in Figure 6 (Figure S-4, Supporting Information, shows the data for 1 mM Li+ solutions). As could already be expected from the data obtained with KLI-1 in solution, an excellent Li+ selectivity was also found for the membrane sensor. No response to any of the possibly interfering ions was observed, and the presence of foreign cations did not hinder the binding of Li+ to the fluoroionophore. The exposure of the membrane to aqueous buffers of varying pH in the physiologically relevant range of pH 6-8 also did not result in any changes of the emission intensity (data not shown), confirming the insensitivity to pH as already demonstrated for KLI-1. The repeatability and the response times for Li+ measurements with the optode membrane were evaluated from the experimental data shown in Figure 6 as well. The response times for a 95% signal change (t95%) were calculated to be 64 ( 8 s (n ) 6) for the forward response from water to 0.1 M Li+ samples (with a background of various foreign ions) and 435 ( 87 s (n ) 6) for the recovery of the original blank signal. It is assumed that these experimental data do not purely reflect the actual response times of the sensing membranes but are to a large extent influenced by the measurement system, such as the flow speed (a constant flow of 1 mL/min was used in all experiments), the dead volume of the flow cell and its tubing, and the geometrical setup of the membrane in the flow cell. A relative loss of the emission signal of 1.25 (deionized water) and 0.21% (0.1 M Li+), respectively, was noted over six cycles. Relative standard deviations of 0.62 (deionized water; n ) 7) and 0.23% (0.1 M Li+; n ) 6) were observed for the fluorescence intensities over six cycles, indicating
a very reproducible response of the sensor despite the presence of various possibly interfering cations. While the sensor suffers from a very small loss of overall signal intensity, the response to Li+ samples remains stable (
